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Printjmc
algebra senior
Problem
Square A and Square B are both by squares. Square A has both its length and width increased by an amount , while Square B has its length and width decreased by the same amount . What is the minimum value of such that the difference in area between the two new squares is at least as great as the area of a by square?
Solution
The new area of Square A is , while the new area of Square B is . The difference in area is For this to be at least as great as the area of a by square, we must have
Final answer
\frac{2009}{4}